Equivalence of turbulence statistics between monodisperse and polydisperse turbidity currents

Abstract

Turbidity currents are buoyancy driven submarine flows where the source of buoyancy is typically a polydisperse sediment suspension. Sustained propagation of such flows depend on the ability of turbulence in the flow to keep the settling sediments in suspension. Recent studies by Cantero et al. (2012b) and Shringarpure et al. (2012) have investigated the interaction of monodisperse sediment suspension and turbulence in turbidity currents on smooth sloping beds. These studies showed that stable stratification of sediment suspension damps turbulence and in some cases can be fully suppress turbulence. Furthermore, it was shown that the turbulence damping effect of a monodisperse sediment suspension can be quantified by the product of shear Richardson number and the sediment settling velocity. In this study we generalize this result for a polydisperse sediment suspension. We compare the turbulence statistics of turbidity currents driven by different polydisperse suspensions and show that as long as the total amount of sediment and the product of shear Richardson number and effective settling velocity (a value representing the polydisperse suspension) are the same, the turbulent velocity statistics of the different polydisperse suspensions nearly collapse. Furthermore, if the effective settling velocity is chosen to be depth-dependent (a function of height from the bed) then the turbulence statistics involving sediment concentration also collapses between different polydisperse suspensions. These results suggest the possibility of modeling polydisperse currents with an equivalent monodisperse suspension whose total sediment load and depth-dependent settling velocity match those of the polydisperse suspension.